Open Number Lines Unit of Study: Strengthening Critical Area: Understanding Place Value to Add and Subtract Global Concept Guide: 2 of 2

Content Development  An open number line is a number line with no numbers or markers. It is a visual representation to track student thinking with mental computation. Using an open number line, students will be able to show the addition or subtraction of tens and ones. Before students use an open number line, they need multiple experiences with a number line with markers and counting on and back within 100.  Click here for more information on open number lines.here

 The Problem: Keisha was trying to set her record for juggling a soccer ball. On her first attempt, she juggled the ball a total of 57 times before it hit the ground. On her second attempt, she only got a total of 29 juggles. Combining both her first and second attempts, how many times did she juggle the ball in total?  When using a number line flexibly, students may choose to solve this problem in any number of ways. Here are three different representations of how students thought differently to solve the problem. The first solution, for example, shows a student who counts on from 57, first by 10ʼs. After skipping forward by 30 (three jumps of 10), the student realizes that she needs to compensate by hopping back by one to arrive at the correct answer

Day 1/2  Day 1 and 2 will focus on how to use the open number line and how it can be used for addition and subtraction problems. Both lessons can be used as a framework and additional problem scenarios can be added for student practice.  It is essential both days focus on addition and subtraction. Day 1 should not focus solely on addition and day 2 focus on subtraction. These operations should be taught together.  Lesson: Adding on an Open Number Line  This lesson provides the teacher model for introduction of an open number line and how students can use this tool to show jumps of tens and ones.  Provide students multiple opportunities to add two digit numbers on an open number line.  This lesson can be used to show the inverse operation, subtraction.  Additional Resource: More Practice Add on Open Number Line

Day 3/4  Day 3 and 4 will focus on the various ways to decompose a number to add and subtract with the open number line.  Provide multiple opportunities for students to share how they used the open number line. It is important for students to see the various ways and explore other ways to decompose numbers.  On day 4, students can share the open number lines and start to recognize similarities and differences with the number lines.  Lesson: Use Problem Solving Scenarios to Add and Subtract with an Open Number Line  Students should be engaged in problem scenarios and real world scenarios (for example, a problem that uses addition and subtraction and it relates to the students’ lives).

Enrich/Reteach/Intervention  Reteach/Intervention  Provide students with addition number sentences listed in the tasks below. Students will solve for the sum utilizing an open number line. The teacher should emphasize the jumps of tens and ones to reinforce place value. Also, provide students practice with subtraction problems, based on the student needs.  Task 1 Task 1  Task 2 Task 2  Enrich  Provide students with addition and subtraction problems and blank open number lines. The students will use this tool to solve the problem but extend their thinking by encouraging more than one way. Students can compare their number lines and find more ways to decompose the numbers.  Provide students with a sample open number line that represents an addition or subtraction problem. Students can create a problem scenario to match the open number line.